A168327 Primes of concatenated form "1 n^3".

11, 127, 12197, 135937, 159319, 11092727, 11295029, 11860867, 12685619, 14330747, 14826809, 15000211, 15929741, 16128487, 18869743, 19393931, 124137569, 126198073, 127818127, 129503629, 138958219, 150243409, 154439939, 160698457, 175686967, 191733851, 195443993

Offset

1,1

Comments

(1) It is conjectured that sequence is infinite.

(2) These are primes all with "leading" digit "1", they are concatenations of two cubic numbers: 1^3 and n^3, n is a natural.

References

Harold Davenport, Multiplicative Number Theory, Springer-Verlag New-York 1980

Leonard E. Dickson: History of the Theory of numbers, vol. I, Dover Publications 2005

Paulo Ribenboim, The New Book of Prime Number Records, Springer 1996

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Formula

If n^3 is a d-digit number and d no multiple of 3, then p=10^d+n^3, where n is odd and no multiple of 5.

a(n) = c+10^A055642(c) where c=A167725(n). - R. J. Mathar, Nov 23 2009

Example

(1) 10^1+1^3=11 = prime(5) = a(1).
(2) 10^2+3^3=127 = prime(31) = a(2).
(3) 10^4+13^3=12197 = prime(1458) = a(3).

Mathematica

Select[FromDigits[Join[{1}, IntegerDigits[#]]]&/@(Range[500]^3), PrimeQ] (* Harvey P. Dale, May 16 2012 *)

Crossrefs

Cf. A168147, A167535.

Sequence in context: A395668 A363111 A181012 * A282042 A015601 A024144

Adjacent sequences: A168324 A168325 A168326 * A168328 A168329 A168330

Keyword

nonn,base

Author

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 23 2009

Extensions

Edited by Charles R Greathouse IV, Apr 24 2010

Status

approved